Laws of nature: Newton's heritage

In this section we will show that there was a specific sense in which Newton influenced Van Musschenbroek's view on laws of nature, most notably in the latter's Dissertatio physica experimentalis de magnete (1729).Footnote ⁴ Newton had established that the law of universal gravitation holds given the laws of motion and that it is able to explain terrestrial as well as celestial motion. The level of unification established hereby was unparalleled. Put differently, Newton had, in his own words, reduced ‘the phenomena of nature to mathematical laws’.Footnote ⁵ Van Musschenbroek embarked on a similar project in his study of magnetism. In his Dissertatio physica experimentalis de magnete, he attempted to establish a mathematical proportion that generally holds between the magnetic force and the minus-nth power of the distance on a par with the law of universal gravitation.Footnote ⁶ As is well documented, given the set-up of his experimental apparatus he did not (and could not) find a general magnetic law comparable to the law of universal attraction and ended up with several spurious laws for different arrangements of pairs of magnets.Footnote ⁷

The picture of the system of the world that emerged after Newton's discoveries was a systema mundi governed by regularity, simplicity and mathematical laws. This led Newton to conclude in the General Scholium, which was added in the second edition of the Principia (1713), that this ‘most elegant system of the sun, planets and comets could not have arisen without the design and dominion of an intelligent and powerful being’.Footnote ⁸ For, as Newton explained in the third edition of the Principia (1726), ‘No variation in things arises from blind metaphysical necessity which must be the same always and everywhere. All the diversity of created things, each in its place and time, could only have arisen from the ideas and the will of a necessarily existing being’.Footnote ⁹ Everything in rerum natura is ‘subordinate to him, and subservient to his Will’.Footnote ¹⁰

In the Opticks Newton distinguished between two kinds of ‘principles’: vis inertiae, on the one hand, which he considered as ‘a passive Principle by which Bodies persist in their Motion or Rest, receive Motion in proportion to the Force impressing it, and resist as much as they are resisted’, and on the other, active principles, ‘such as that of Gravity, and that which causes Fermentation, and the Cohesion of Bodies’.Footnote ¹¹ As one notices, in this context ‘principles’ refers to kinds of force. Since ‘very little Motion in the World’ results from the vis inertiae of bodies, which is ‘accompanied with such passive Laws of Motion as naturally result from that Force’, active principles are required to put bodies in motion.Footnote ¹² Newton commented as follows on the active principles:

As can be seen, Newton was convinced that motion and activity in the natural world could be accounted for by a limited number of principles – ‘two or three’.

To summarize, in Newton's natural philosophy laws of nature play a prominent role. In this context, laws of nature were conceived as universal statements that, on the one hand, make claims about a type of force that has been demonstrated to exist, and, on the other, stipulate how that force varies mathematically in relation to other quantities. Both aspects can be found in Van Musschenbroek's work around 1729. In Dissertatio physica experimentalis de magnete he stated that in the case of attraction we can show by experiments that such ‘cause of motion’ (‘causa motus’) exists, but that we cannot know the modus operandi of this cause.Footnote ¹⁴ Furthermore, as we have seen, it was his endeavour to establish a ‘law of nature’ that governed magnetic phenomena by looking for a mathematical relation between the force of magnetism and its relation to other relevant quantities. For Newton, as long as a type of force had been demonstrated to exist, it did not matter that the cause of such force was unknown in order for the force itself to be explanatory. It should be noted that Newton conceived of forces as causes, which can be seen, for instance, from his statement in Opticks that ‘the main Business of natural Philosophy is to argue from Phænomena without feigning Hypotheses, and to deduce Causes from Effects’.Footnote ¹⁵ In addition, he wrote that we proceed ‘from Motions to the Forces producing them; and in general, from Effects to Causes’, thereby equating forces with causes.Footnote ¹⁶ The laws of nature are, according to Newton, the effect of God's will.

Van Musschenbroek's 1723 oration: immutable causal relations lege à Deo statuta

On 13 September 1723 Van Musschenbroek delivered an oration at the University of Utrecht on the occasion of his taking up the position of professor of philosophy and mathematics.Footnote ¹⁷ It was here that Van Musschenbroek first used the term ‘law’. At that point he used the term ‘law’ simpliciter rather than ‘law of nature’. Throughout his oration, entitled De certa methodo philosophiae experimentalis, he explicitly proclaimed that it was his aim to defend the method of experimental philosophy and to criticize the a priori method of Descartes.Footnote ¹⁸ Thus he signalled that he was bringing a new programme of experimental philosophy and physics to the University of Utrecht. Although there had been some interest in experimentation and observation at the University of Utrecht, his call for an experimental philosophy based on the systematic collection of a vast amount of observational and experimental histories, on the one hand, and on the rejection of hypotheses, on the other, was new. Before his arrival, experiments and observations were made in an Aristotelian or a Cartesian framework. His predecessor, Johannes Luyts, for instance, was a vindicator of Aristotle and an opponent of Descartes with an interest in astronomy.Footnote ¹⁹ The work of Van Musschenbroek's colleague Joseph(us) Serrurier, on the other hand, testifies to a sympathy for Descartes's (natural) philosophy. Serrurier was appointed in 1706 as professor of philosophy and mathematics, a position he kept until 1716, when he became professor of medicine and botany.

Van Musschenbroek begins his oration by observing that natural philosophy has been unstable because the opinions defended in it have been in a state of perpetual flux.Footnote ²⁰ The reason for this is that natural philosophy has been based on a priori reasoning. Natural philosophy based on the a priori method is ‘uncertain, wanting and transient’ (‘incerta, manca, fluxa’).Footnote ²¹ According to Van Musschenbroek, since there are no innate ideas, and all our ideas originate from sensory impressions, the basis of our knowledge is to be sought in observation and experimentation. The internal substances of bodies cannot be known, but we can know their attributes.Footnote ²² In order to acquire this knowledge, observations and experiments need to be supplanted with mathematics. By means of mathematics we will be able to draw certain conclusions from a firm foundation of experiments and observations.Footnote ²³ When our ideas of the attributes of bodies represent quantities, they can be treated mathematically. This leads to a mathematical physics in which the relations that hold between those quantities are explored. We should therefore seek knowledge of nature through a combination of gathering observational and experimental data, and mathematical reasoning based on these data.Footnote ²⁴ If philosophers in the past had taken more care in compiling ‘experimental histories’ (‘historiae experimentales’) than in ‘indulging in their own reasonings’, we would not have seen so many controversies between them.Footnote ²⁵ This is because such histories provide us with data, ‘which always are, have been, and will remain, most true’.Footnote ²⁶

Later on in the oration, Van Musschenbroek underscores the certainty of experimental philosophy and the lack of controversies within the community of those who practise it. He then links the certainty that is attainable in experimental philosophy to the notion of a ‘law’:

That the order and stability of nature depends on God had already been incorporated by Van Musschenbroek in the very definition of experimental physics (physica experimentalis), provided at the beginning of the oration. There, he stated that the ultimate goal of this discipline is to arrive at a demonstration of ‘the first cause, infinitely powerful, and most wise, out of whose immense generosity [and] incomprehensible force all things flow, and by whom they are maintained and conserve the most elegant order that is achieved in all [their] parts’.Footnote ²⁸ To conclude, in his 1723 oration Van Musschenbroek defended the view that the systematic collection of observational and experimental histories, when combined with mathematics, provides certain knowledge because the effects studied in it are produced by causes which always remain the same by a divine law.

Epitome elementorum physico-mathematicorum (1726): laws as empirical regularities

In Van Musschenbroek's first physics textbook, Epitome elementorum physico-mathematicorum, the notion of a ‘law’ is explicitly discussed in the introductory chapter.Footnote ²⁹ The notion of a ‘law of nature’ appeared further on in the Epitome.Footnote ³⁰ As mentioned above, Van Musschenbroek's textbooks should be seen as one and the same work which he updated, revised and extended throughout his career. The changes Van Musschenbroek made therefore allow us to trace the development of his thinking on the subject of laws of nature.

In the first chapter of this book, Van Musschenbroek discusses the nature of philosophy, puts forward the sub-discipline of ‘physics’ (‘physica’) as the proper subject matter of the book, and then devotes several paragraphs to a discussion of laws.Footnote ³¹ The term appears for the first time in the definition of mechanics, which is ‘the part of physics, which teaches according to which laws of motion bodies are being changed, or act and are moved’.Footnote ³² Van Musschenbroek then continues with an explicit definition of the term ‘law’: ‘By “law” we understand the same as the rule, according to which God wanted that in the most constant way phenomena of that sort happen in such conditions of bodies’.Footnote ³³ Note the absence of causal talk. Although further on in the Epitome Van Musschenbroek refers to Newton's theory of universal gravitation as a law of nature, when he actually defines the concept ‘law’ his focus is on the laws of motion. The term ‘phenomena’ was itself defined in the preceding paragraphs, and is to be understood as any sensory observation.Footnote ³⁴ Given this definition of phenomena, we can take the laws (of motion)/the laws of nature in Van Musschenbroek's sense to be empirical regularities. This stands in contrast to Newton's reading of the laws of nature. As we saw in the previous section, according to Newton, these laws identify forces of a generic sort that he considered the (proximate) causes of effects. Newton was concerned with both the proximate causes of motion, i.e. gravitational forces, and the remote cause of motion, i.e. the cause of gravity.Footnote ³⁵ He only made statements on the cause of gravity in a speculative context, in the Queries to the Opticks, for instance. In a demonstrative context – most notable in the Principia – Newton remained agnostic with respect to the remote cause of motion.Footnote ³⁶ Van Musschenbroek, by contrast, was agnostic with respect to both the proximate and the remote causes of effects.

In the paragraph immediately following this definition, Van Musschenbroek incorporates and elaborates on the points made in his 1723 oration. Laws can only be discovered through sensory observation. Because of their constant character, these laws, when known, allow us to foresee events. He illustrates this with the example of a wedge: if we see a wedge splitting a piece of wood today, we can expect the same kind of wedge to be able to split a similar piece of wood tomorrow.Footnote ³⁷ If laws were not constant ‘our thinking would be submitted to perpetual doubts’.Footnote ³⁸ As in the oration, Van Musschenbroek also stresses the importance of compiling a ‘history’ (‘historia’) of data. He now posits it explicitly as a prerequisite for establishing the universality of laws:

In a passage further on in the book, in a chapter on the mutual attraction between bodies, Van Musschenbroek writes that (gravitational) attraction is to be conceived as ‘a law of nature instilled in bodies by the Creator’, which ‘depends only on the divine will’.Footnote ⁴⁰ In a related passage, reminiscent of Newton's words, he remarks that he does not consider attraction ‘as an occult quality arising from the specific form of the greater bodies, but as a universal law of nature’.Footnote ⁴¹ He concludes the section on laws by repeating that whoever wants to posit ‘general laws’ (‘leges generales’) should collect observations of ‘all the changes of all bodies’ (‘omnes mutationes omnium corporum’).Footnote ⁴² The study of physics is ‘inexhaustible’ (‘inexhaustum’), because the bodies to be studied are ‘almost infinite in number’.Footnote ⁴³

1734–1741: voluntarism and general versus special laws

In 1734, a new edition of Van Musschenbroek's textbook was published, this time under the title Elementa physicae conscripta in usus academicos. The overall organization and contents of the introductory chapter remain the same, with some salient changes and additions. To the objects studied by physics, space (spatium) is now added alongside bodies and motion.Footnote ⁴⁴ Van Musschenbroek again states that all changes are due to the interaction between bodies, but rather than concluding that bodies and motion are the proper object of study of physics, he now concludes that ‘the most preferable object for physics is motion’.Footnote ⁴⁵ Immediately after this sentence comes the paragraph that contained the definition of ‘law’ in the previous edition. This paragraph is now heavily reworked:

In the second edition of the Elementa physicae (1741), the following addition is made after the first sentence: ‘We call laws constant phenomena that, whenever bodies are placed in similar circumstances, always occur in the same way’.Footnote ⁴⁷ The paragraph on laws continues with a passage on the advantage of knowing laws, and the example of the wedge, which was discussed above. Another example of a law is, however, added to that of the wedge: when we see that a mustard seed sown in fertile ground produces rich crops this year, we can expect it to do the same next year in similar circumstances.Footnote ⁴⁸ The example of animals and plants shows that Van Musschenbroek's focus is no longer exclusively on the laws of motion and the law of universal gravitation, but also on the laws governing the plant and animal kingdoms. The passage on sensory observation as the only source for our knowledge of laws is also greatly expanded. Van Musschenbroek now explicitly counterposed the empirical approach towards discovering the laws of nature against the a priori approach. He defends the former by emphasizing the dependence of the laws of nature on the will of God:

In other words, because God is free to create the world in different ways we are bound to investigate which laws obtain in our universe empirically. A priori reasoning is to no avail in this context. Here also, Van Musschenbroek inserts the same examples to explain what is meant by the statement ‘that certain motions are always executed on the same occasions’: from one kind of seed the same kind of plant always grows, animals generate other animals similar to themselves, bodies striking each other exchange motion in a determinate manner.Footnote ⁵⁰ A short passage is also added mentioning another advantage provided by the knowledge of laws: by knowing them, we can distinguish miracles from natural events, for miracles are contrary to the laws.Footnote ⁵¹ In his annotations to Beginselen der natuurkunde Van Musschenbroek states that ‘we do not know the supernatural, unless we have first learned the natural’.Footnote ⁵² As in the previous edition, he discusses the vast scope of physics and the need to make many empirical observations before one is able to put forward laws. However, he now adds an explicit reason for this: ‘This should be done, however, because nature abounds in such a great variety: we should not establish [laws as] general laws that are only singular [laws]’.Footnote ⁵³ As an example of this, Van Musschenbroek refers to the generation of certain insects and plants. He concludes with regard to the example of plants that ‘several laws obtain in the vegetable kingdom’.Footnote ⁵⁴

The introductory chapter is now concluded with a brief mention of Newton's rules of philosophizing (regulae philosophandi).Footnote ⁵⁵ These rules are the methodological guidelines which Newton had provided in his Principia.Footnote ⁵⁶ Further in this paper, we will show how after 1748 Van Musschenbroek expressed reservations with regard to the rule on the use of analogy in natural philosophy. These reservations are related to his changing views on laws of nature.

The passage in the Epitome in which Van Musschenbroek states that the law of universal attraction is dependent on the free will of God is reworked: he now states that gravitational attraction and attraction in general are caused by ‘active principles’ (‘Principia activa’) that are imparted by the ‘Omnipotent Creator’.Footnote ⁵⁷ Van Musschenbroek's statement that the laws of nature are dependent on ‘the most free will of the Creator’ has an important anti-Spinozist dimension. Remedying the dangers of Benedict Spinoza's necessitarian ideas was a typical and widespread Dutch preoccupation.Footnote ⁵⁸ In Corollary 1 to Proposition 32 of Part I of the Ethics, according to which the ‘will cannot be called a free cause, but only a necessary one’, Spinoza argued that ‘God does not produce any effect by freedom of the will’ (‘Deum non operari ex libertate voluntatis’).Footnote ⁵⁹ Here ‘freedom of the will’ is to be understood as a will that is absolutely free.Footnote ⁶⁰ The proposition that immediately follows states, ‘Things could have been produced by God in no other way, and in no other order than they have been produced’, for, as Spinoza argued, if things were produced by God in a different way or order ‘then God's nature could also have been other than it is now, and therefore … that [other nature] would also have to exist, and consequently, there could have been two or more Gods, which is absurd’.Footnote ⁶¹ Spinoza's necessitarian system in which there is no room for God's (absolute) free will was a matter of great concern to Van Musschenbroek. In a series of lectures which he delivered in 1725, he vehemently objected to Spinoza's system.Footnote ⁶² In these lectures he drew extensively on the anti-Spinozist arguments in Samuel Clarke's A Demonstration of the Being and Attributes of God (1705). More precisely, Van Musschenbroek denounced Spinoza's view that God is determined ‘by natural necessity without will and deliberation’ (‘naturali necessitate, absque voluntate et arbitrio’)Footnote ⁶³ and he castigated Corollary 1 to Proposition 32 and Proposition 33, Part I.Footnote ⁶⁴ By emphasizing that the laws of nature depend for their existence on an arbitrary act of the free will of God, Van Musschenbroek tried to steer clear of conferring any absolute necessity on the laws of nature.

In 1736 a Dutch translation of the Elementa was published, entitled Beginselen der natuurkunde. A second edition of this translation appeared under the title Beginsels der natuurkunde in 1739. The translation remains faithful to the Latin original, although a few passages are added to the text. In the passage quoted above, where Van Musschenbroek treated our ignorance of the causes underlying laws, he now adds that he would rather confess his ignorance (onkunde) than ‘claim with vanity already to know how from a mustard seed an entire plant grows, and that this happened through the mechanical powers of the seed itself’, without having duly examined the matter.Footnote ⁶⁵ On the constancy of the laws of nature he states, ‘These laws are always constantly the same, because what is more constant than the will of God upon which they depend? If they were unstable, man would be very unhappy’.Footnote ⁶⁶ Van Musschenbroek's claim that the laws of nature are constant because they depend on God's constant will seems difficult to square with the thesis that one can straightforwardly distinguish between naturalia and miracula. If miracles, i.e. events contrary to the laws of nature, indeed occur, then God's will seems inconstant. This stands in tension with his key argument for the constancy of the laws of nature.Footnote ⁶⁷ Here one could, for instance, invoke the Malebranchean argument, according to which there is a difference between God's ‘general volitions’, by which he installs constant laws, and his ‘particular volitions’, as a result of which miracles occur. Unfortunately, Van Musschenbroek remained silent on how the constancy of God's will and the occurrence of miracles were to be harmonized.

The Dutch translation provides a further clarification with regard to the distinction between ‘general laws’ and ‘singular laws’, which was made in the 1734 Latin text. Van Musschenbroek again emphasizes the need to investigate bodies of many different kinds before we can put forward general laws (algemeene Wetten). These general laws show ‘that it pleases the Almighty, to preserve the creation, and make it work’.Footnote ⁶⁸ He adds a reference to the number of species found in Conrad Gesner's work as an example of the vastness of nature and therefore the inexhaustible nature of physics.Footnote ⁶⁹ We should take care, Van Musschenbroek says, not to presume too quickly to have found general laws. Experience shows ‘that there are many special laws [byzondere wetten], and fewer general [ones]’.Footnote ⁷⁰ For example, it seems to be a general law that animals are born directly out of eggs. When a chicken egg hatches, a chick appears that develops into a chicken. However, when the eggs of bloodless animals hatch a worm appears that first changes into a pupa that then changes into a fly. These are examples of ‘special laws, which one can only learn through experience, by investigating every species separately’.Footnote ⁷¹ Van Musschenbroek inserts a reference to the work of René-Antoine de Réaumur on the moth and to that of Gottfried Sell(ius) on the woodworm as examples.Footnote ⁷² In the second edition of the Dutch translation, the passage on the special laws is significantly expanded with even more examples and references to relevant contemporary literature.Footnote ⁷³ These additions are to be found in Van Musschenbroek's annotated copy of Beginselen der natuurkunde.Footnote ⁷⁴ He also adds a call for an intellectual division of labour. If every scholar were to focus his or her energy on the study of one species, we would much faster attain our goal of ‘a more perfect knowledge of all laws of nature’.Footnote ⁷⁵ At this point we can discern two general trends in the development of the contents of the introduction to the textbook. On the one hand, there is a growing emphasis on the existence of special laws and the need for a case-by-case (or, more exactly, a species-by-species) investigation of nature. Related to this, there is a growing concern for examples from natural history and the incorporation of references to contemporary literature in that field. The focus on special laws emerged at least in part from Van Musschenbroek's expanding knowledge of the diversity of nature through natural history. It is possible that Van Musschenbroek also came to doubt the possibility of finding general laws as a result of his study of magnetism. In a manuscript probably composed around 1740, he writes that he ‘is absolutely not convinced that the same and universal law obtains in all magnets which the earth carries’.Footnote ⁷⁶ This shows how natural-philosophical research (including his own) had an impact on his characterization of laws of nature.

1748–1762: the methodological significance of polyps and laws nostri respectu

In 1748, another edition of Van Musschenbroek's textbook was brought on the market, this time under the title Institutiones physicae conscriptae in usus academicos. Again, not only the title, but also some of its contents, had changed. With regard to the concept of law, the following changes are salient. First of all, whereas in all previous editions Van Musschenbroek defined the term ‘laws’, he now writes ‘laws of nature’ (‘leges naturae’).Footnote ⁷⁷ Although the term already occurred in previous editions, it is now the first time that it is used as definiendum. As we saw in the previous section, Van Musschenbroek came to emphasize that there are not only laws that govern inert bodies, but also laws that regulate the plant and animal kingdoms. It is plausible that he introduced the term ‘law of nature’ to highlight this. Apart from this change, the definition is identical to the definition in the second edition of Elementa. The paragraph which previously contained the discussion of the concepts of ‘general’ and ‘singular laws’ is heavily reworked in this edition. The terms are now entirely absent, as are the examples mentioned in the previous editions. Van Musschenbroek still emphasizes the need to investigate all the bodies in the different kingdoms (mineral, vegetable, animal and atmospheric), and replaces the examples with a list of all the subdivisions within these kingdoms.Footnote ⁷⁸ He again emphasizes the need to investigate all different species separately, and to refrain from hasty generalization, but without relying on the concept of a ‘singular’ or ‘special’ law:

Related to this, in the annotated copy of Institutiones, Van Musschenbroek states that Newton's third rule of philosophizing, which legitimized the use of analogical reasoning in natural philosophy, cannot be universally applied ‘as (John Turberville) Needham [1713–1781] has excellently shown [optime monente Needhamo]’.Footnote ⁸⁰ Here he is referring to a paper of Needham which was published in 1748, in which he warned against the unwarranted use of analogy.Footnote ⁸¹ The gist of these annotations would later make its way into his Introductio ad philosophiam naturalem.Footnote ⁸² Van Musschenbroek's reservation concerning the universal applicability of Rule 3 stemmed in part from the biological research to which he was exposed.Footnote ⁸³ Especially significant was the case of an aquatic polyp which he observed himself in the summer of 1742.Footnote ⁸⁴ In his annotated copy of Beginsels, he notes that when such a polyp is cut into pieces each of its parts evolves into polyps similar to the original polyp.Footnote ⁸⁵ In the same series of annotations, he also mentions Abraham Trembley's discovery of the famous hydra polyp, which showed that polyps grow out of one another like branches that grown on a tree. Van Musschenbroek furthermore mentions that on the back of some water insects a new one grows until it is fully formed and falls off. Some insects split into different parts that each develop into insects similar to the original one.Footnote ⁸⁶ What he learned from all this was that, contrary to his 1739 belief that all animals are generated viviparously or oviparously, species are generated in a multitude of ways. From a methodological perspective this meant that since nature does things in different ways we ought to be very careful when using analogical reasoning. In his Oratio de divina sapientia (Oration on the Divine Wisdom) (1744), Van Musschenbroek spelled out the theological ramifications of the mysterious generation of polyps: it indicates ‘that God wanted to show us, insignificant beings, that he accomplishes, wills and enables the same goal not in one simple way, but in several ways’.Footnote ⁸⁷

Together with the disappearance of the terms ‘singular’ and ‘general’ laws, came the appearance of the concept ‘laws with respect to us’. In the paragraph containing the discussion of the dependence of natural laws on the incomprehensible, free volition of God, and our ignorance with regard to causes, Van Musschenbroek added the following passage:

The last edition of the textbook, which was published posthumously in 1762 under the title Introductio ad philosophiam naturalem (Introduction to Natural Philosophy), showed Van Musschenbroek increasingly engaged in theological issues. In previous editions, he was content merely to mention that ‘every plant produces its own seed’, and that ‘every animal is generated from its like’ as examples of laws.Footnote ⁸⁹ Now, a whole page is added to these statements. These additions include a summary of observations which prove that a seed of a plant does indeed bring forth the same plant and no other.Footnote ⁹⁰ These facts, according to Van Musschenbroek, have important ramifications. They show

The passage devoted to the notion of ‘laws with respect to us’ is also expanded, adding important clarifications:

Van Musschenbroek now introduces a distinction between so-called ‘primary or general laws’, which are laws depending immediately on the will of God, and ‘secondary or specific laws’, which depend on the ‘primary laws’. He immediately points out, however, that from our human perspective we cannot distinguish between them. Therefore we cannot know which laws are ultimately primary. Van Musschenbroek thus considers the search for the underlying causal structure of nature a futile endeavour. In his annotated copy of Beginsels der natuurkunde, Van Musschenbroek confessed that his desire to search for the causes of phenomena was ‘the only old yeast of the Cartesian philosophy’ (‘eenige oude zuurdeessem van de Cartesiaansche Philosophie’) still remaining in him.Footnote ⁹³ If we link this with the concepts of ‘general’ and ‘special laws’ used by Van Musschenbroek in the previous editions of the textbook, we can state that ‘special laws’ are effects of more ‘general’ laws, so that they in principle could be subsumed under these laws if we had further knowledge. But as we can never know whether we have reached ontological ‘rock bottom’ and have finally found ‘general laws’, the distinction between ‘general laws’ and ‘special laws’ seems somewhat problematic. Every ‘special law’ could in the end turn out to be subsumable under a ‘general law’, but the latter could in the end turn out to be itself another ‘special law’ subsumable under an even more general one. By using the term ‘laws with respect to us’ and by defining these as laws that cannot be subsumed under broader laws given the current state of our knowledge, Van Musschenbroek seems to have found a way to evade this problem. The term ‘with respect to us’ is now also put to work in the paragraph on miracles, to which the following passage was added:

In this way, Van Musschenbroek could seemingly brush aside discussions on the status of miracles in a law-governed universe as vacuous. As in previous textbooks, other additions demonstrate his continual engagement with state-of-the-art research in natural history and the life sciences. References are made to articles in the Journal des sçavans, L'histoire de l'Académie royale, and the Philosophical Transactions.Footnote ⁹⁵ The list of subdivisions within the different kingdoms of nature is also much expanded and refined.Footnote ⁹⁶ We have seen that in the Institutiones Van Musschenbroek pointed out that ‘the knowledge of one species does not allow you to draw conclusions about other ones’. In the Introductio he now introduces a paragraph on the risks of inductive generalization or analogia after his discussion of Newton's regulae philosophandi.

In 1762 an abbreviated version of Van Musschenbroek's Introductio was published posthumously under the title Compendium physicae experimentalis conscriptum in usus academicos. Here, his views on laws of nature are summarized in the following short paragraph:

Van Musschenbroek's continued belief that the laws of nature were contingent set him apart from an important French tradition that sought to highlight that the laws and principles of nature were necessary.Footnote ⁹⁸ The work of Maupertuis deserves to be mentioned in this context. In a paper published in 1748, Maupertuis demonstrated that the laws governing the behaviour of colliding bodies and the law of mechanical equilibrium could be derived from what he called a ‘general principle’ (‘principe général’).Footnote ⁹⁹ This principle has become known as the ‘principle of least action’: ‘Whenever a change happens in nature, the quantity of action necessary for this change, is as small as possible.’Footnote ¹⁰⁰ The derivation of these laws from the principle of least action could be seen as an example of the subsumption of laws under a more general law. In his own annotated copy of the Institutiones, Van Musschenbroek referred to Maupertuis's principle, but did not describe it as a general law to which less general laws are to be subsumed. Van Musschenbroek makes his comment on Maupertuis's principle in an addition to the passage in the textbook on the laws of collision, not in relation to his earlier remarks on laws of nature at the beginning of the textbook. Van Musschenbroek explicitly mentions Maupertuis's principle as an extra principle that can be added to the laws already discussed, rather than as a more general law.Footnote ¹⁰¹ In the end only a short reference to Maupertuis's article made its way into the posthumously published new version of the textbook.Footnote ¹⁰² In any case, his engagement with Maupertuis's principle did not lead him to doubt his adherence to the contingency of the laws of nature.